THE COST OF ACHIEVING THE BEST PORTFOLIO IN HINDSIGHT

Erik Ordentlich and Thomas M. Cover

Chapter 16 in The Kelly Capital Growth Investment Criterion:Theory and Practice, 2011, pp 211-233 from World Scientific Publishing Co. Pte. Ltd.

Abstract: For a market with m assets consider the minimum, over all possible sequences of asset prices through time n, of the ratio of the final wealth of a nonanticipating investment strategy to the wealth obtained by the best constant rebalanced portfolio computed in hindsight for that price sequence. We show that the maximum value of this ratio over all nonanticipating investment strategies is Vn = [∑ 2−nH(n1/n, …, nm/n)(n !/(n1 ! ⋯ nm !))]−1, where H(·) is the Shannon entropy, and we specify a strategy achieving it. The optimal ratio Vn is shown to decrease only polynomially in n, indicating that the rate of return of the optimal strategy converges uniformly to that of the best constant rebalanced portfolio determined with full hindsight. We also relate this result to the pricing of a new derivative security which might be called the hindsight allocation option.

Keywords: Kelly Criterion; Dynamic Investment Analysis; Capital Growth Theory; Sports Betting; Hedge Fund Strategies; Speculative Investing; Fortune 's Formula (search for similar items in EconPapers)
Date: 2011
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